The slain agent was identified by a Border Patrol official as Nicholas Ivie, 30, KPHO-TV, Phoenix, reported.
Ivie was one of three agents investigating a ground sensor that had been triggered about 7 miles east of Bisbee, Ariz., when they reported by radio about 1:50 a.m. they were under fire. When deputies arrived, Ivie was dead and another agent, whose name had not been released, had serious but not life-threatening injuries, said Carol Capas, a Cochise County Sheriff's Office spokeswoman.
No suspects were in custody and she could not provide information on the shooters.
"His thoughts and prayers, and our thoughts and prayers go out to the family members of the border agent who was killed, as well as to the agent who was wounded," Carney said.
The agents were assigned to the Brian Terry Station in Naco, Ariz., named after an agent who was killed on duty at the border in 2010, The Arizona Republic reported Tuesday.
"Last night's events demonstrate the danger that law enforcement officers face along the Southwest border every day," James Turgill, special agent in charge of the FBI for the Phoenix division, said at an afternoon news briefing.
"Ivie was doing his job, protecting the border in the line of duty."
Homeland Security Secretary Janet Napolitano ordered all DHS flags to fly at half-staff in honor of Ivie, who leaves behind a wife and two children.